Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.2s (37.4%)

Results

915.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify227.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series17.0ms (0.6%)

Counts

3 → 18

Calls

3 calls:

10.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
6.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
1.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 6 x -6)
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

simplify88.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune70.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
	1.4b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	22.9b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 1389 to 1004 computations (27.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.1b	(fma.f64 6 x -6)
✓	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series22.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
10.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 71

Calls

2 calls:

5.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
2.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

simplify104.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

780×	`distribute-rgt-in_binary64`
765×	`distribute-lft-in_binary64`
466×	`fma-neg_binary64`
286×	`fma-def_binary64`
279×	`div-sub_binary64`

Counts

77 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	1535
1	136	1358
2	379	1358
3	1052	1339
4	2953	1339
5	3780	1339
6	4677	1339
7	4954	1339

prune121.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
▶	1.4b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	22.9b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 3198 to 2370 computations (25.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6)))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6)))
✓	0.7b	(cbrt.f64 (fma.f64 6 x -6))

series23.0ms (0.7%)

Counts

4 → 39

Calls

4 calls:

12.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6)))
5.0ms	(cbrt.f64 (fma.f64 6 x -6))
2.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6)))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
6.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6)))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6)))
1.0ms	(cbrt.f64 (fma.f64 6 x -6))

simplify100.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

802×	`times-frac_binary64`
405×	`fma-def_binary64`
313×	`fma-neg_binary64`
242×	`cancel-sign-sub-inv_binary64`
169×	`distribute-rgt-in_binary64`

Counts

157 → 228

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	3198
1	517	2872
2	1761	2490
3	4543	2429
4	5008	2429

prune308.0ms (9.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	322	0	322
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	322	4	326

Error

Counts

326 → 4

Alt Table

Status	Error	Program
✓	1.4b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	22.9b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 10974 to 8671 computations (21% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.2b	(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))
✓	1.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	21.6b	(/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series44.0ms (1.4%)

Counts

4 → 21

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
14.0ms	(.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
10.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
2.0ms	(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary64`
47×	`add-exp-log_binary64`
30×	`pow1_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
7.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
4.0ms	(.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
3.0ms	(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/r*_binary64`
411×	`distribute-rgt-in_binary64`
397×	`distribute-lft-in_binary64`
377×	`associate-*l/_binary64`
200×	`associate-/l/_binary64`

Counts

132 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	5923
1	286	2497
2	1154	2213
3	4954	2213

prune160.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
✓	1.4b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (cbrt.f64 (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	22.9b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 7039 to 5030 computations (28.5% saved)

regimes355.0ms (11.4%)

Accuracy

Total 0.1b remaining (47.1%)

Threshold costs 0.1b (47.1%)

Counts

142 → 1

Compiler

Compiled 6573 to 5190 computations (21% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	18	19
2	20	19
3	21	19
4	20	19

end101.0ms (3.2%)

Compiler: Compiled 124 to 96 computations (22.6% saved)

Details

analyze5.0ms (0.2%)

sample1.2s (37.4%)

simplify227.0ms (7.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series17.0ms (0.6%)

rewrite5.0ms (0.2%)

simplify88.0ms (2.8%)

prune70.0ms (2.3%)

localize10.0ms (0.3%)

series22.0ms (0.7%)

rewrite13.0ms (0.4%)

simplify104.0ms (3.3%)

prune121.0ms (3.9%)

localize12.0ms (0.4%)

series23.0ms (0.7%)

rewrite25.0ms (0.8%)

simplify100.0ms (3.2%)

prune308.0ms (9.9%)

localize15.0ms (0.5%)

series44.0ms (1.4%)

rewrite37.0ms (1.2%)

simplify76.0ms (2.4%)

prune160.0ms (5.1%)

regimes355.0ms (11.4%)

simplify2.0ms (0.1%)

end101.0ms (3.2%)

Profiling